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This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials.

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13-17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry...